We have conducted a coordinated series of theoretical studies and analysis of experiments regarding hormone receptor interactions. The theoretical studies seek to develop appropriate mathematical models for the description of hormone-receptor interactions and occupancy-response coupling. A variety of model biological systems have been used to develop and test these mathematical models, including opioid peptides binding to their receptors, glucocorticoid binding to receptors, GABA, muscimol, and glutamate binding. By development of appropriate mathematical models and computer programs for curve fitting and data analysis, we have been able to characterize several of these complex ligand receptor systems. These often involve multiple receptor states or multiple receptor subtypes. Special attention has been given to the case of multiple ligands reacting simultaneously with multiple classes of sites, and the interaction of divalent ligands with cell surface receptors. The mathematical and statistical theory of radioimmunoassay and related techniques have been under development. We have been interested in the enzyme multiplied immunological technique (EMIT), the enzyme-linked-immuno-absorbent assay (ELISA), and chemiluminescent assays. The mathematical theory of optimization of RIA, and appropriate computer programs for data analysis and quality control have been further developed.